R Notebook

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Set the base directory for your analysis

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library(BSFG)

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The following code generates simulated data, and then loads it into the R workspace

can be skipped if you are loading your own data in a different way

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seed = 1  # for reproducibility
nSire = 50 # simulation design is a half-sib design: each of nSire fathers has nRep children, each with a different female
nRep = 10
nTraits = 100
nFixedEffects = 2 # fixed effects are effects on the factors
nFactors = 10
factor_h2s = c(rep(0,nFactors/2),rep(0.9,nFactors/2))  # factor_h2 is the % of variance in each factor trait that is explained by additive genetic variation.
# The is after accounting for the fixed effects on the factors
Va = 2 # residual genetic variance in each of the observed traits after accounting for the factors
Ve = 2 # residual microenvironmental variance in each of the observed traits after accounting for the factors
Vb = 0 # magnitude of the fixed effects (just factors)
new_halfSib_simulation('Sim_FE_1', nSire=nSire,nRep=nRep,p=nTraits, b=nFixedEffects, factor_h2s= factor_h2s,Va = Va, Ve = Ve,Vb = Vb)
set.seed(seed)
load('setup.RData')

Y = setup$Y
data = setup$data
K = setup$K
Y[1:(nrow(Y)*3/4),1:(ncol(Y)/4)] = NA
# Y[(nrow(Y)/4)+1:(nrow(Y)/4),(ncol(Y)/4)+1:(ncol(Y)/4)] = NA
# Y[2*(nrow(Y)/4)+1:(nrow(Y)/4),2*(ncol(Y)/4)+1:(ncol(Y)/4)] = NA
# Y[3*(nrow(Y)/4)+1:(nrow(Y)/4),3*(ncol(Y)/4)+1:(ncol(Y)/4)] = NA

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Set the parameters of the BSFG model

see ?BSFG_control

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run_parameters = BSFG_control(
  num_NA_groups = 3,
  scale_Y = FALSE,   # should the columns of Y be re-scaled to have mean=0 and sd=1?
  simulation = TRUE, # Are you running against simulated data (ex from a call to new_halfSib_simulation above)? If so, you can provide the setup list and it will make some QC plots
  h2_divisions = 20, # Each variance component is allowed to explain between 0% and 100% of the total variation. How many segments should the range [0,100) be divided into for each random effect?
  h2_step_size = NULL, # if NULL, all possible values of random effects are tried each iteration. If in (0,1), a new candidate set of random effect proportional variances is drawn uniformily with a range of this size
  burn = 00,  # number of burn in samples before saving posterior samples
  K = 15 # number of factors
)

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Set the prior hyperparameters of the BSFG model

see ?BSFG_control

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priors = BSFG_priors(
  tot_Y_var = list(V = 0.5,   nu = 5),      # Prior variance of trait residuals after accounting for fixed effects and factors
  tot_F_var = list(V = 18/20, nu = 20),     # Prior variance of factor traits. This is included to improve MCMC mixing, but can be turned off by setting nu very large
  Lambda_prior = list(
    sampler = sample_Lambda_prec_horseshoe,
    prop_0 = 0.1,
    delta_l = list(shape = 3, rate = 1),
    delta_iterations_factor = 100
  ),
  B2_prior = list(
    sampler = sample_B2_prec_horseshoe,
    prop_0 = 0.1
  ),
  cis_effects_prior = list(
    prec = 1
  ),
  h2_priors_resids_fun = function(h2s,n)  1,  # Function that returns the prior density for any value of the h2s vector (ie the vector of random effect proportional variances across all random effects. 1 means constant prior. Alternative: pmax(pmin(ddirichlet(c(h2s,1-sum(h2s)),rep(2,length(h2s)+1)),10),1e-10),
  h2_priors_factors_fun = function(h2s,n) 1 # See above. Another choice is one that gives 50% weight to h2==0: ifelse(h2s == 0,n,n/(n-1))
)

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Construct the model

see ?BSFG_init

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options(error=recover)
BSFG_state = setup_model_BSFG(Y,            # n x p data matrix
                              ~(1|animal),  # RHS of base model for factors and residuals. Fixed effects defined here only apply to the factor residuals.
                              extra_regressions = list(X = model.matrix(~Fixed1,data)[,-1,drop=FALSE],factors=T,resids=F), # design matrix for additional fixed effects. These coefficients will be regularized with the B2_prior above. The same model can be used for both factors and resids
                              data,         # the data.frame with information for constructing the model matrices
                              relmat = list(animal = K), # covariance matrices for the random effects. If not provided, assume uncorrelated
                              run_parameters=run_parameters,
                              setup = setup, # only if running simulated data. Stores simulated values for comparison
                              run_ID = 'BSFG_example'
                                )

'BSFG_example' already exists

maps = make_Missing_data_map(BSFG_state,50,0,T)

  iter N_groups max_group_size total_kept_NAs
1    2        2            125              0

BSFG_state = set_Missing_data_map(BSFG_state,maps$Missing_data_map_list[[maps$map_results$iter[which(maps$map_results$total_kept_NAs ==0)[1]]]])
BSFG_state = set_priors_BSFG(BSFG_state,priors)
BSFG_state = initialize_variables_BSFG(BSFG_state)

[1] "initializing Lambda_prec regularized horseshoe"
[1] "initializing B_prec regularized horseshoe"

BSFG_state = initialize_BSFG(BSFG_state)

[1] "Pre-calculating random effect inverse matrices for 2 groups of traits and 20 sets of random effect weights"

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BSFG_state = clear_Posterior(BSFG_state)

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Run MCMC

see ?sample_BSFG

A MCMC chain is a way of fitting parameters from a Bayesian model

The chain is a sequence of draws from the Posterior distribution of each parameter.

BSFG uses a Gibbs sampler, which means that we iterate through all of the model’s parameters

and for each parameter draw a new value from it’s posterior holding all other parameters constant

This works, but the individual draws are not independent draws from the joint posterior of all parameters.

Therefore, to get independent draws, we have to collect many posterior samples, and then save only a portion of them.

Also, it may take many iterations for the MCMC chain to converge to the central part of the distribution.

This is the burnin period, and we do not store these values (they are not useful).

At the end, we have a collection of samples from the posterior distribution of each parameter.

We can use these samples to characterize each distribution: mean, SD, histogram, HPDinterval, etc.

The way BSFG works is that you ask the program to collect a small number of samples

And then can assess how the chain is performing (how well it is mixing, is it converged?)

And then either save the samples as posterior samples, or declare them as burn-in and discard them.

Then, you can ask for more samples, and repeat until you have enough.

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Tools for re-setting Posterior samples, and helping chain converge

BSFG_state = clear_Posterior(BSFG_state)

BSFG_state = reorder_factors(BSFG_state)

n_samples = 200;  # how many samples to collect at once?
for(i  in 1:70) {
  print(sprintf('Run %d',i))
  BSFG_state = sample_BSFG(BSFG_state,n_samples,grainSize=1)  # run MCMC chain n_samples iterations. grainSize is a paramter for parallelization (smaller = more parallelization)
  
  BSFG_state = save_posterior_chunk(BSFG_state)  # save any accumulated posterior samples in the database to release memory
  print(BSFG_state) # print status of current chain
  plot(BSFG_state) # make some diagnostic plots. These are saved in a pdf booklet: diagnostic_plots.pdf
  # set of commands to run during burn-in period to help chain converge
  if(BSFG_state$current_state$nrun < BSFG_state$run_parameters$burn || i < 10) {
    BSFG_state = reorder_factors(BSFG_state,drop_cor_threshold = 0.6) # Factor order doesn't "mix" well in the MCMC. We can help it by manually re-ordering from biggest to smallest
    BSFG_state = clear_Posterior(BSFG_state)
    print(BSFG_state$run_parameters$burn)
  }
}

[1] "Run 1"

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Time difference of 5.461753 secs

 Current iteration: 200, Posterior_samples: 100 
 Current factor dimension: 15 factors 
 Total time: 5.461753 secs 

[1] 200
[1] "Run 2"

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Time difference of 5.272238 secs

 Current iteration: 400, Posterior_samples: 100 
 Current factor dimension: 15 factors 
 Total time: 10.73399 secs 

[1] 400
[1] "Run 3"

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Time difference of 5.195707 secs

 Current iteration: 600, Posterior_samples: 100 
 Current factor dimension: 15 factors 
 Total time: 15.9297 secs 

[1] 600
[1] "Run 4"

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Time difference of 5.247838 secs

 Current iteration: 800, Posterior_samples: 100 
 Current factor dimension: 15 factors 
 Total time: 21.17754 secs 

[1] 800
[1] "Run 5"

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Time difference of 5.169021 secs

 Current iteration: 1000, Posterior_samples: 100 
 Current factor dimension: 15 factors 
 Total time: 26.34656 secs 

[1] 1000
[1] "Run 6"

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Time difference of 5.19673 secs

 Current iteration: 1200, Posterior_samples: 100 
 Current factor dimension: 15 factors 
 Total time: 31.54329 secs 

[1] 1200
[1] "Run 7"

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Time difference of 5.396714 secs

 Current iteration: 1400, Posterior_samples: 100 
 Current factor dimension: 15 factors 
 Total time: 36.94 secs 

[1] 1400
[1] "Run 8"

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Time difference of 5.337378 secs

 Current iteration: 1600, Posterior_samples: 100 
 Current factor dimension: 15 factors 
 Total time: 42.27738 secs 

[1] 1600
[1] "Run 9"

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Time difference of 5.398423 secs

 Current iteration: 1800, Posterior_samples: 100 
 Current factor dimension: 15 factors 
 Total time: 47.6758 secs 

[1] 1800
[1] "Run 10"

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Time difference of 5.180273 secs

 Current iteration: 2000, Posterior_samples: 100 
 Current factor dimension: 15 factors 
 Total time: 52.85608 secs 

[1] "Run 11"

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Time difference of 5.71851 secs

 Current iteration: 2200, Posterior_samples: 200 
 Current factor dimension: 15 factors 
 Total time: 58.57458 secs 

[1] "Run 12"

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Time difference of 5.361292 secs

 Current iteration: 2400, Posterior_samples: 300 
 Current factor dimension: 15 factors 
 Total time: 1.065598 mins 

[1] "Run 13"

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Time difference of 4.924132 secs

 Current iteration: 2600, Posterior_samples: 400 
 Current factor dimension: 15 factors 
 Total time: 1.147667 mins 

[1] "Run 14"

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Time difference of 4.918461 secs

 Current iteration: 2800, Posterior_samples: 500 
 Current factor dimension: 15 factors 
 Total time: 1.229641 mins 

[1] "Run 15"

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Time difference of 4.845258 secs

 Current iteration: 3000, Posterior_samples: 600 
 Current factor dimension: 15 factors 
 Total time: 1.310395 mins 

[1] "Run 16"

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Time difference of 4.919252 secs

 Current iteration: 3200, Posterior_samples: 700 
 Current factor dimension: 15 factors 
 Total time: 1.392383 mins 

[1] "Run 17"

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Time difference of 5.044489 secs

 Current iteration: 3400, Posterior_samples: 800 
 Current factor dimension: 15 factors 
 Total time: 1.476458 mins 

[1] "Run 18"

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Time difference of 4.90688 secs

 Current iteration: 3600, Posterior_samples: 900 
 Current factor dimension: 15 factors 
 Total time: 1.558239 mins 

[1] "Run 19"

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Time difference of 4.806394 secs

 Current iteration: 3800, Posterior_samples: 1000 
 Current factor dimension: 15 factors 
 Total time: 1.638346 mins 

[1] "Run 20"

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Time difference of 4.858743 secs

 Current iteration: 4000, Posterior_samples: 1100 
 Current factor dimension: 15 factors 
 Total time: 1.719325 mins 

[1] "Run 21"

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Time difference of 4.866929 secs

 Current iteration: 4200, Posterior_samples: 1200 
 Current factor dimension: 15 factors 
 Total time: 1.80044 mins 

[1] "Run 22"

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Time difference of 4.796507 secs

 Current iteration: 4400, Posterior_samples: 1300 
 Current factor dimension: 15 factors 
 Total time: 1.880382 mins 

[1] "Run 23"

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Time difference of 4.874933 secs

 Current iteration: 4600, Posterior_samples: 1400 
 Current factor dimension: 15 factors 
 Total time: 1.961631 mins 

[1] "Run 24"

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Time difference of 4.989547 secs

 Current iteration: 4800, Posterior_samples: 1500 
 Current factor dimension: 15 factors 
 Total time: 2.04479 mins 

[1] "Run 25"

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Time difference of 4.866584 secs

 Current iteration: 5000, Posterior_samples: 1600 
 Current factor dimension: 15 factors 
 Total time: 2.1259 mins 

[1] "Run 26"

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Time difference of 4.966299 secs

 Current iteration: 5200, Posterior_samples: 1700 
 Current factor dimension: 15 factors 
 Total time: 2.208671 mins 

[1] "Run 27"

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Time difference of 4.860971 secs

 Current iteration: 5400, Posterior_samples: 1800 
 Current factor dimension: 15 factors 
 Total time: 2.289688 mins 

[1] "Run 28"

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Time difference of 4.862408 secs

 Current iteration: 5600, Posterior_samples: 1900 
 Current factor dimension: 15 factors 
 Total time: 2.370728 mins 

[1] "Run 29"

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Time difference of 4.727269 secs

 Current iteration: 5800, Posterior_samples: 2000 
 Current factor dimension: 15 factors 
 Total time: 2.449516 mins 

[1] "Run 30"

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Time difference of 4.93302 secs

 Current iteration: 6000, Posterior_samples: 2100 
 Current factor dimension: 15 factors 
 Total time: 2.531733 mins 

[1] "Run 31"

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Time difference of 4.825589 secs

 Current iteration: 6200, Posterior_samples: 2200 
 Current factor dimension: 15 factors 
 Total time: 2.612159 mins 

[1] "Run 32"

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Time difference of 4.940678 secs

 Current iteration: 6400, Posterior_samples: 2300 
 Current factor dimension: 15 factors 
 Total time: 2.694504 mins 

[1] "Run 33"

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Time difference of 4.863957 secs

 Current iteration: 6600, Posterior_samples: 2400 
 Current factor dimension: 15 factors 
 Total time: 2.77557 mins 

[1] "Run 34"

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Time difference of 4.875252 secs

 Current iteration: 6800, Posterior_samples: 2500 
 Current factor dimension: 15 factors 
 Total time: 2.856824 mins 

[1] "Run 35"

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Time difference of 4.819959 secs

 Current iteration: 7000, Posterior_samples: 2600 
 Current factor dimension: 15 factors 
 Total time: 2.937156 mins 

[1] "Run 36"

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Time difference of 4.973731 secs

 Current iteration: 7200, Posterior_samples: 2700 
 Current factor dimension: 15 factors 
 Total time: 3.020052 mins 

[1] "Run 37"

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Time difference of 4.93479 secs

 Current iteration: 7400, Posterior_samples: 2800 
 Current factor dimension: 15 factors 
 Total time: 3.102298 mins 

[1] "Run 38"

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Time difference of 4.921592 secs

 Current iteration: 7600, Posterior_samples: 2900 
 Current factor dimension: 15 factors 
 Total time: 3.184325 mins 

[1] "Run 39"

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Time difference of 4.763582 secs

 Current iteration: 7800, Posterior_samples: 3000 
 Current factor dimension: 15 factors 
 Total time: 3.263718 mins 

[1] "Run 40"

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Time difference of 4.814238 secs

 Current iteration: 8000, Posterior_samples: 3100 
 Current factor dimension: 15 factors 
 Total time: 3.343955 mins 

[1] "Run 41"

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Time difference of 4.734801 secs

 Current iteration: 8200, Posterior_samples: 3200 
 Current factor dimension: 15 factors 
 Total time: 3.422869 mins 

[1] "Run 42"

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Time difference of 4.713998 secs

 Current iteration: 8400, Posterior_samples: 3300 
 Current factor dimension: 15 factors 
 Total time: 3.501435 mins 

[1] "Run 43"

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Time difference of 4.803699 secs

 Current iteration: 8600, Posterior_samples: 3400 
 Current factor dimension: 15 factors 
 Total time: 3.581497 mins 

[1] "Run 44"

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Time difference of 5.008898 secs

 Current iteration: 8800, Posterior_samples: 3500 
 Current factor dimension: 15 factors 
 Total time: 3.664979 mins 

[1] "Run 45"

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Time difference of 4.931475 secs

 Current iteration: 9000, Posterior_samples: 3600 
 Current factor dimension: 15 factors 
 Total time: 3.74717 mins 

[1] "Run 46"

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Time difference of 4.953587 secs

 Current iteration: 9200, Posterior_samples: 3700 
 Current factor dimension: 15 factors 
 Total time: 3.82973 mins 

[1] "Run 47"

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Time difference of 4.269113 secs

 Current iteration: 9400, Posterior_samples: 3800 
 Current factor dimension: 15 factors 
 Total time: 3.900882 mins 

[1] "Run 48"

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Time difference of 4.42522 secs

 Current iteration: 9600, Posterior_samples: 3900 
 Current factor dimension: 15 factors 
 Total time: 3.974635 mins 

[1] "Run 49"

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Time difference of 4.38351 secs

 Current iteration: 9800, Posterior_samples: 4000 
 Current factor dimension: 15 factors 
 Total time: 4.047694 mins 

[1] "Run 50"

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Time difference of 4.603884 secs

 Current iteration: 10000, Posterior_samples: 4100 
 Current factor dimension: 15 factors 
 Total time: 4.124425 mins 

[1] "Run 51"

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Time difference of 4.437119 secs

 Current iteration: 10200, Posterior_samples: 4200 
 Current factor dimension: 15 factors 
 Total time: 4.198377 mins 

[1] "Run 52"

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Time difference of 4.448249 secs

 Current iteration: 10400, Posterior_samples: 4300 
 Current factor dimension: 15 factors 
 Total time: 4.272515 mins 

[1] "Run 53"

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Time difference of 4.419041 secs

 Current iteration: 10600, Posterior_samples: 4400 
 Current factor dimension: 15 factors 
 Total time: 4.346165 mins 

[1] "Run 54"

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Time difference of 4.457382 secs

 Current iteration: 10800, Posterior_samples: 4500 
 Current factor dimension: 15 factors 
 Total time: 4.420455 mins 

[1] "Run 55"

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Time difference of 4.269126 secs

 Current iteration: 11000, Posterior_samples: 4600 
 Current factor dimension: 15 factors 
 Total time: 4.491607 mins 

[1] "Run 56"

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Time difference of 4.263794 secs

 Current iteration: 11200, Posterior_samples: 4700 
 Current factor dimension: 15 factors 
 Total time: 4.56267 mins 

[1] "Run 57"

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Time difference of 4.418482 secs

 Current iteration: 11400, Posterior_samples: 4800 
 Current factor dimension: 15 factors 
 Total time: 4.636312 mins 

[1] "Run 58"

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Time difference of 4.433291 secs

 Current iteration: 11600, Posterior_samples: 4900 
 Current factor dimension: 15 factors 
 Total time: 4.7102 mins 

[1] "Run 59"

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Time difference of 4.216706 secs

 Current iteration: 11800, Posterior_samples: 5000 
 Current factor dimension: 15 factors 
 Total time: 4.780478 mins 

[1] "Run 60"

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Time difference of 4.999487 secs

 Current iteration: 12000, Posterior_samples: 5100 
 Current factor dimension: 15 factors 
 Total time: 4.863803 mins 

[1] "Run 61"

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Time difference of 4.30007 secs

 Current iteration: 12200, Posterior_samples: 5200 
 Current factor dimension: 15 factors 
 Total time: 4.935471 mins 

[1] "Run 62"

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Time difference of 4.305386 secs

 Current iteration: 12400, Posterior_samples: 5300 
 Current factor dimension: 15 factors 
 Total time: 5.007227 mins 

[1] "Run 63"

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Time difference of 4.424619 secs

 Current iteration: 12600, Posterior_samples: 5400 
 Current factor dimension: 15 factors 
 Total time: 5.080971 mins 

[1] "Run 64"

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Time difference of 4.25061 secs

 Current iteration: 12800, Posterior_samples: 5500 
 Current factor dimension: 15 factors 
 Total time: 5.151814 mins 

[1] "Run 65"

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Time difference of 4.388198 secs

 Current iteration: 13000, Posterior_samples: 5600 
 Current factor dimension: 15 factors 
 Total time: 5.224951 mins 

[1] "Run 66"

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Time difference of 4.202981 secs

 Current iteration: 13200, Posterior_samples: 5700 
 Current factor dimension: 15 factors 
 Total time: 5.295001 mins 

[1] "Run 67"

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Time difference of 4.524976 secs

 Current iteration: 13400, Posterior_samples: 5800 
 Current factor dimension: 15 factors 
 Total time: 5.370417 mins 

[1] "Run 68"

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Time difference of 5.562619 secs

 Current iteration: 13600, Posterior_samples: 5900 
 Current factor dimension: 15 factors 
 Total time: 5.463127 mins 

[1] "Run 69"

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Time difference of 4.332948 secs

 Current iteration: 13800, Posterior_samples: 6000 
 Current factor dimension: 15 factors 
 Total time: 5.535343 mins 

[1] "Run 70"

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Time difference of 4.721933 secs

 Current iteration: 14000, Posterior_samples: 6100 
 Current factor dimension: 15 factors 
 Total time: 5.614042 mins 

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Work with the Posterior samples

———————————————————-